On the time-dependent analysis of Gamow decay

Dürr, D., Grummt, R. and Kolb, M. (2011) On the time-dependent analysis of Gamow decay. European Journal of Physics, 32 (5). pp. 1311-1321. ISSN 1361-6404 doi: 10.1088/0143-0807/32/5/019

Abstract/Summary

Gamow's explanation of the exponential decay law uses complex 'eigenvalues' and exponentially growing 'eigenfunctions'. This raises the question, how Gamow's description fits into the quantum mechanical description of nature, which is based on real eigenvalues and square integrable wavefunctions. Observing that the time evolution of any wavefunction is given by its expansion in generalized eigenfunctions, we shall answer this question in the most straightforward manner, which at the same time is accessible to graduate students and specialists. Moreover, the presentation can well be used in physics lectures to students.